In Exodus 12:40-41, we find this very specific statement:
40 The time that the Israelites had lived in Egypt was four hundred and thirty years. 41 At the end of four hundred and thirty years, on that very day, all the companies of Yahweh went out from the land of Egypt.
The problem is that this is at odds with the genealogy in Exodus 6:16-20:
16 The following are the names of the sons of Levi according to their genealogies: Gershon, Kohath, and Merari, and the length of Levi's life was one hundred and thirty-seven years. 17 The sons of Gershon: Libni and Shimei, by their families. 18 The sons of Kohath: Amram, Izhar, Hebron, and Uzziel, and the length of Kohath's life wasone hundred and thirty-three years. 19 The sons of Merari: Mahli and Mushi. These are the families of the Levites according to their genealogies. 20 Amram married Jochebed his father's sister and she bore him Aaron and Moses, and the length of Amram's life was one hundred and thirty-seven years.
The most time in Egypt that the Exodus-6 genealogy allows is around 350 years, and this is being as generous as possible by assuming that Kohath was only an infant when he entered Egypt (we know from Genesis 46:11 that he had already been born) and that both he and his son Amram, father of Moses and Aaron, sired children in the last years of their lives. The circa-350-years figure comes from adding the ages of Kohath and Amram when they died to Moses' age at the exodus. (Exodus 7:7 says, "Moses was eighty years old and Aaron eighty-three when they spoke to Pharaoh.") We know that Moses was still only 80 when he actually led the exodus, since he died at the age of 120 (Deuteronomy 34:7), and the Israelites wandered for 40 years under Moses' leadership (Ex. 16:35, Nu. 14:26-34, Deut. 8:2; Acts 13:18).
This is a big discrepancy in itself, but the problem doesn't end there, because Genesis 15:13-16 contains a "prophecy" about the Egyptian enslavement:
13 Then Yahweh said to Abram, 'Know this for certain, that your offspring shall be aliens in a land that is not theirs, and shall be slaves there, and they shall be oppressed for four hundred years; 14 but I will bring judgement on the nation that they serve, and afterwards they shall come out with great possessions. 15 As for yourself, you shall go to your ancestors in peace; you shall be buried in a good old age. 16 And they shall come back here in the fourth generation; for the iniquity of the Amorites is not yet complete.'
Stephen's speech in Acts 7 refers to this passage and its prediction of 400 years of affliction:
6 And God spoke in these terms, that his descendants would be resident aliens in a country belonging to others, who would enslave them and maltreat them for four hundred years. 7 "But I will judge the nation that they serve," said God, "and after that they shall come out and worship me in this place."
Obviously, if the Israelites were only in Egypt for at most around 350 years, then they couldn't have been oppressed for 400 years, even if they were oppressed the entire time that they were in Egypt, which they were not. Genesis 41:46 states that Joseph was 30 when he came to power: "Joseph was thirty years old when he entered the service of Pharaoh king of Egypt." Genesis 50:26 says that he died at age 110: "And Joseph died, being one hundred ten years old..." Joseph, then, ruled for 80 years (110-30=80). After Joseph rose to power, there were seven years of plenty followed by seven years of famine (Genesis 41:29 ff), and the Israelites were told to enter Egypt two years into the years of famine (Genesis 45:6-12), which would be the ninth year after Joseph rose to power. 80 years of Joseph's rule, minus nine years before the Israelites arrived, means that for around 70 years (perhaps a year elapsed from the time the Israelites left Canaan until their arrival in Egypt), the Israelites lived in Egypt without being enslaved (see Exodus 1:6 ff), and this is just taking Joseph's age into consideration. We know from Genesis 29:30-35 that Levi was born to Leah at some point during Jacob's second seven-year period of service to Laban, and Genesis 30:24-25 states that Joseph was born shortly before the end of those seven years, so Levi was perhaps five years or so older than Joseph. Exodus 1:6 says that Joseph and all his brothers died before the enslaving pharaoh came to power, and since Levi died at age 137 (Exodus 6:16) and Joseph at 110 (see above), an additional 20 or so years can be added to the around 70 that they were in Egypt without oppression.
There are two main approaches that biblical inerrantists take to "solve" the contradiction between the Exodus-6 genealogy and Exodus 12:40. They either claim that the Exodus-6 genealogy isn't complete or they assert that the Septuagint (and Samaritan Pentateuch) reading of Exodus 12:40, which says that 430 years includes time in Egypt and Canaan (cf. Galatians 3:17), is to be preferred, shortening the time in Egypt to around 200 years. Jews claim that only 210 years were spent in Egypt. All approaches are problematic, however, and none explains how the Israelites could be oppressed for 400 years "in a land that is not theirs" (in other words, not Canaan, a land given to Abraham's descendants [Genesis 15:18]), when at most they were oppressed for around 340 years (see above) or even much less if the 430 years is alleged to include time in Canaan. I can present biblical and extrabiblical evidence which shows that the Exodus-6 genealogy is intended to convey literal father-son relationships, and shortening the time in Egypt to circa 200 years only exacerbates the conflict between Genesis 15 and Exodus 12:40.